Answer:
<h2><em><u>Pythagorean </u></em><em><u>theorem </u></em><em><u>reads </u></em><em><u>as:</u></em></h2><h2><em><u>H²</u></em><em><u>=</u></em><em><u>P²</u></em><em><u>+</u></em><em><u>B</u></em><em><u>²</u></em></h2><h2><em><u>in </u></em><em><u>which </u></em><em><u>p </u></em><em><u>reads </u></em><em><u>as </u></em><em><u>perpendicular </u></em><em><u>so </u></em></h2><h2><em><u>P²</u></em><em><u>=</u></em><em><u>H²</u></em><em><u>-</u></em><em><u>B²</u></em></h2><em><u></u></em>
Amie's error while measuring the volume of a sphere is that <u>Amie should have multiplied 54 by 2/3</u>. Thus, the <u>first option</u> is the right choice.
In the question, we are given that a sphere and a cylinder have the same radius and height.
We assume the radius of the sphere to be r, and its height to be h.
Now, the height of a sphere is its diameter, which is twice the radius.
Thus, the height of the sphere, h = 2r
Given that the sphere and the cylinder have the same radius and height, the radius of the cylinder is r, and its height is 2r.
The volume of a sphere is given by the formula, V = (4/3)πr³, where V is its volume, and r is its radius.
Thus, the volume of the given sphere using the formula is (4/3)πr³.
The volume of a cylinder is given by the formula, V = πr²h, where V is its volume, r is its radius, and h is its height.
Thus, the volume of the given cylinder using the formula is πr²(2r) = 2πr³.
Now, to compare the two volumes we take their ratios, as
Volume of the sphere/Volume of the cylinder
= {(4/3)πr³}/{2πr³}
= 2/3.
Thus, the volume of the sphere/the volume of the cylinder = 2/3,
or, the volume of the sphere = (2/3)*the volume of the cylinder.
Given the volume of the cylinder to be 54 m³, Amie should have multiplied 54 by 2/3 instead of adding the two.
Thus, Amie's error while measuring the volume of a sphere is that <u>Amie should have multiplied 54 by 2/3</u>. Thus, the <u>first option</u> is the right choice.
Learn more about volumes at
#SPJ4
For the complete question, refer to the attachment.
